Lattice calculation of αs in momentum scheme

We compute the flavorless running coupling constant of QCD from the three gluon vertex in the (regularisation independent) momentum subtraction renormalisation scheme. This is performed on the lattice with high statistics. The expected color dependence of the Green functions is verified. There are significant O(a(2)mu(2)) effects which can be consistently controlled. Scaling is demonstrated when the renormalisation scale is varied between 2.1 GeV and 3.85 GeV. Scaling when the lattice spacing is varied is very well satisfied. The resulting flavorless conventional two loop Lambda(c)/MS is estimated to be, respectively for the MOM and M (O) over tilde M scheme, 361(6) MeV and 345(6) MeV, while the three loop results are, depending on beta(2): Lambda(3)/MS = (412-59 beta(2)/beta(2,<(MS)over bar>) +/- 6 MeV) and Lambda(3)/MS = (382 - 46 beta(2)/beta(2,<(MS)over bar>) +/- 5 MeV). A preliminary computation of beta 2 in the M (O) over tilde M scheme leads to Lambda(3)/MS = 303(5) a(-1)(beta=6.0)/1.97GeV MeV.